A subsidiary of the State Capital Investment Corporation (SCIC) was unable to buy 225,000 VNM shares, or a 0.01 percent stake, due to "market volatility", according to a Vinamilk statement on Friday.
SCIC is the largest shareholder in Vinamilk with a 36 percent stake.
F&N Dairy Investments Pte Ltd failed to buy 17.41 million shares, or nearly 1 percent, between July 17 and August 14. It already owns 17.69 percent.
Another company, Platinum Victory Pte Ltd, too failed to buy a nearly 1 percent stake and its ownership stays at 10.62 percent.
Both Singaporean companies have registered again to buy in September. They have been seeking to increase their stakes in Vinamilk repeatedly since early 2018 but in vain.
Vinamilk saw first half pre-tax profit rise by 3 percent year-on-year to over VND7 trillion ($302 million).
CEO Mai Kieu Lien said earlier the company had stocked ingredients so that it could have an advantage when trade is disrupted by travel bans.
The company, which holds half the Vietnamese dairy market, last year acquired a majority stake in a competitor, Moc Chau Milk, and has recently announced plans to set up a cafe chain in Vietnam and increase its investment in a Laotian subsidiary.